分段二次保极值的保形插值方法

Piecewise quadratic spline interpolation with shape and extremum preserved

现有保形插值方法一般都是基于单调数组给出的,未能解决非单调数组的保形保极值插值问题.针对任意给定的数组,将其划分为几个单调区间,并根据型值点的一二阶差商特性,适当的插入新的节点及配置各节点的导数值,给出了一种既保形又保极值的一阶光滑的分段二次插值函数的构造方法.最后通过Matlab给出了几个具有代表性的算例及其图形结果.

Since the existing interpolation methods with shape preserving are all based on the monotonous data, they cannot solve the interpolation problems in which both the shape and extremum are preserved for the non-monotonous data. In this paper, an interpolation method with shape and extremum preserving is presented. The method consists of several steps. First, the given data are divided into several monotonous intervals. Then some new nodes are inserted with some appropriately derivative values tbr each node according to the characteristic of the first and the second order divided differences. Finally, a piecewise quadratic interpolation method is suggested which can guarantee that the first derivative of the resulting function is continuous. In the end, several representative examples and their interpolation graphical results are given by Matlab.